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The equation of the curve shown in the xy-plane above is
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06 Jun 2021, 22:20
06 Jun 2021, 22:20
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Question Stats:
69% (01:31) correct
30% (01:30) wrong based on 72 sessions
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The equation of the curve shown in the xy-plane above is \( 9x^2+16y^2=144\). Points A, B, C, and D are the x- and y-intercepts of the graph.
Quantity A |
Quantity B |
Length AB |
Length CD |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The equation of the curve shown in the xy-plane above is
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06 Jun 2021, 23:36
06 Jun 2021, 23:36
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Carcass wrote:
Attachment:
GRE circle.png
The equation of the curve shown in the xy-plane above is \( 9x^2+16y^2=144\). Points A, B, C, and D are the x- and y-intercepts of the graph.
Quantity A |
Quantity B |
Length AB |
Length CD |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Put \(y = 0\) in the equation to find the x-intercepts
\( 9x^2 = 144\)
\( x^2 = \frac{144}{9}\)
\( x = \sqrt{\frac{144}{9}}\)
\(x = ±\frac{12}{3} = ±4\)
i.e. B = (4, 0) and A = (-4, 0)
Now, Put \(x = 0\) in the equation to find the y-intercepts
\( 16y^2 = 144\)
\( y^2 = \frac{144}{16}\)
\( y = \sqrt{\frac{144}{16}}\)
\(y = ±\frac{12}{4} = ±3\)
i.e. C = (3, 0) and D = (-3, 0)
Col. A: 4 + 4 = 8
Col. B: 3 + 3 = 6
Hence, option A
Re: The equation of the curve shown in the xy-plane above is
[#permalink]
30 Oct 2024, 05:10
30 Oct 2024, 05:10
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